MAT 205 CHECKPOINT 5
MAT 205 CHECKPOINT 5
POINT VALUES
|SECTION 5.1 |SECTION 5.2 |SECTION 5.3 |
|Question |Points |Question |Points |Question |Points |
|1 |2 |1 |2 |1 |2 |
|2 |2 |2 |2 |2 |2 |
|3 |2 |3 |2 |3 |2 |
|4 |2 |4 |2 |4 |2 |
|5 |2 |5 |2 |5 |2 |
Most the problems in this checkpoint involve the straightforward use of financial formulas. It is required that you show your work for every problem. At a minimum this includes showing the formula used, and showing the values substituted in the pertinent places of the formula to get your answer. If you simply write the final answer, no credit will be given.
For example, if you feel that the right formula for a problem is the simple interest formula, you need to state that the formula to be used is i=Prt, and then substitute the numbers given for P, r, and t into the formula, to calculate the interest result.
You do not, in general, need to show a lot of intermediate calculations. This is of course a math course, so if you show the right formula, put the right values in, but get the wrong answer, you will not get full credit.
Section 5.1
5.1-1) What investment has to be initially made to result in $2000 in 8 years if the return is 9% compounded semi annually?
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5.1-2) Alvin borrows $25,900 to start a bike shop, and repays the loan after 11 months with an interest of 8.4%. How much was the repayment?
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5.1-3) A $100,000 certificate of deposit held for 60 days returns $101,133.33. What was the interest rate, to the nearest tenth of a percent?
|The answer here depends on how frequently the interest is compounded: |
| |
|Daily based on a 360 day year: |
| |
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| |
| |
|Daily based on a 365 day year: |
| |
|[pic] |
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|Monthly: |
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5.1-4) A certain bacteria population grows at the rate of 2% per hour in a growth medium. Find the number of hours it takes for the population to double. (Hint: one way to do this is to use Excel)
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5) A young boy invests $1 in 1950 in an account that is compounded quarterly at $%. How much is the account worth in 2010?
|Assuming that the interest rate was intended to be 4%: |
|[pic] |
Section 5.2
5.2-1) Find the future value of an ordinary annuity with payments of $3700 compounded semi annually at 8% for 11 years.
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5.2-2) Find the future value of this annuity due. $750 deposited at the beginning of each month, for 15 years, compounded at 5.9% monthly.
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5.2-3) Find the amount of each payment to be made in a sinking fund to accumulate $8500. The money earns 8% compounded annually, with 7 annual payments.
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5.2-4) A company plan puts $1000 into an employee’s savings account on his first day of employment. Each year on the employee’s service anniversary $1000 is also deposited. The employee leaves after 21 exact years of service, and a $1000 deposit is made at that time. The account earns 9.5% compounded annually. What is the account value on the day the employee leaves?
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5.2-5) From age 40 to 65 an employee deposits $2000 a year in an IRA. The deposits are made semiannually at the end of each semiannual period. The IRA earns 4% with semiannual compounding. What is the final account value?
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Section 5.3
5.3-1) Find the present value of an ordinary annuity with payments of $10,000 semiannually for 15 years at 10% compounded semiannually.
|[pic] |
5.3-2) Find the payment needed to amortize $140,000 at 12% compounded quarterly with 15 quarterly payments.
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5.3-3) George buys a lawn mower for $600 down and monthly payments of $30 for 3 years. The interest rate on the unpaid balance is 1.25% per month. Find the cost of the mower and the total interest paid.
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5.3-4) Martin buys a used car for $4000 and amortizes the used car loan in 4 annual payments at 8% compounded annually. Prepare an amortization schedule, using Excel, showing the first 4 payments of the loan. Make columns showing the Payment Number, the Payment Amount, the Interest For Period, the portion of the payment that Goes To Principal, and the Principal at End of Period.
|Payment |
|Payment |
|Beginning |
|Interest |
|Principal |
|Ending |
| |
|Number |
|Amount |
|Balance |
|For Period |
|Payment |
|Principal |
| |
|1 |
|$1,207.68 |
|$4,000.00 |
|$320.00 |
|$887.68 |
|$3,112.32 |
| |
|2 |
|$1,207.68 |
|$3,112.32 |
|$248.99 |
|$958.70 |
|$2,153.62 |
| |
|3 |
|$1,207.68 |
|$2,153.62 |
|$172.29 |
|$1,035.39 |
|$1,118.23 |
| |
|4 |
|$1,207.68 |
|$1,118.23 |
|$89.46 |
|$1,118.23 |
|$0.00 |
| |
5.3-5) Prepare an amortization schedule for a loan of $37947.50 with interest at 8.5% compounded annually, to be paid with equal payments over 10 years. Use Excel, show the first 10 payments of the loan. Make columns showing the Payment Number, the Payment Amount, the Interest For Period, the portion of the payment that Goes To Principal, and the Principal at End of Period.
|Payment |
|Payment |
|Beginning |
|Interest |
|Principal |
|Ending |
| |
|Number |
|Amount |
|Balance |
|For Period |
|Payment |
|Principal |
| |
|1 |
|$470.49 |
|$37,947.50 |
|$268.79 |
|$201.70 |
|$37,745.80 |
| |
|2 |
|$470.49 |
|$37,745.80 |
|$267.37 |
|$203.13 |
|$37,542.67 |
| |
|3 |
|$470.49 |
|$37,542.67 |
|$265.93 |
|$204.57 |
|$37,338.10 |
| |
|4 |
|$470.49 |
|$37,338.10 |
|$264.48 |
|$206.02 |
|$37,132.09 |
| |
|5 |
|$470.49 |
|$37,132.09 |
|$263.02 |
|$207.48 |
|$36,924.61 |
| |
|6 |
|$470.49 |
|$36,924.61 |
|$261.55 |
|$208.95 |
|$36,715.67 |
| |
|7 |
|$470.49 |
|$36,715.67 |
|$260.07 |
|$210.43 |
|$36,505.24 |
| |
|8 |
|$470.49 |
|$36,505.24 |
|$258.58 |
|$211.92 |
|$36,293.33 |
| |
|9 |
|$470.49 |
|$36,293.33 |
|$257.08 |
|$213.42 |
|$36,079.91 |
| |
|10 |
|$470.49 |
|$36,079.91 |
|$255.57 |
|$214.93 |
|$35,864.98 |
| |
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